It is well known (see, for example, § 2.5.3 of [1]}) that for \(\lbrace s_{k}\rbrace =\lbrace 2^{ks}\rbrace \)  and \(p,q \in (0,\infty ]\) 
the spaces \(\widetilde{B}^{l}_{p,q,p}(\mathbb {R}^{n},\lbrace s_{k}\rbrace )\)  and \(B^{\lbrace s_k\rbrace }_{p,q}(\mathbb {R}^{n})\)  coincide when
\(s > n\max \lbrace \frac{1}{p}-1,0\rbrace \) . However, if \(s < n\max \lbrace \frac{1}{p}-1,0\rbrace \) , then the space \(B^{\lbrace s_k\rbrace }_{p,q}(\mathbb {R}^{n})\) 
(unlike the space \(\widetilde{B}^{l}_{p,q,p}(\mathbb {R}^{n},\lbrace t_{k}\rbrace )\) ) contains
the Dirac delta function. In this section we shall establish the relation between the spaces \(\widetilde{B}^{l}_{p,q,r}(\mathbb {R}^{n},\lbrace t_{k}\rbrace )\)  and
\(B^{\varphi _{0}}_{p,q}(\mathbb {R}^{n},\lbrace t_{k}\rbrace )\)  under minimal assumptions
on the variable smoothness \(\lbrace t_{k}\rbrace \) .
